Numerous magnet applications require provision of a magnetic field on the inside or the outside of a cylindrical structure with a varied number of magnetic poles. Examples of such applications are use of magnets for charged particle beam optics such as used in particle accelerator applications, particle storage rings, beam lines for the transport of charged particle beams from one location to another, and spectrometers to spread charged particle beams in accord with particle mass. Magnets of various multi pole orders are needed for charged particle beam optics. In such charged particle beam applications dipole magnets are needed for steering the particle beam, quadrupoles are needed for focusing the beam, and higher-order multi pole magnets provide the optical equivalent of chromatic corrections.
Any field errors (i.e., deviations from the ideal field strength distribution for a given application) in such systems are known to degrade the performance of the beam optics, leading to a rapid increase in beam cross sections, or beam loss within the system. In the case of mass spectrometry, field uniformity is a limiting factor in the ability to separate particles of differing masses. Analogous to light optical systems, for which the lenses conform to predefined geometries and are ground accordingly with very high precision to render satisfactory resolution of the transmitted image, the invention is based on recognition that optimal performance of magnets in charged particle beam systems is dependent on creation of optimal and practical conductor winding configurations and achievement of mechanical tolerances to which the fabricated systems conform to the predefined configurations.
In some applications using charged particle beam optics, magnetic fields of modest strength, e.g., less than 2 Tesla, are required. In these instances, the shapes of the iron poles which are magnetized with current-carrying windings are highly determinative of the field quality. That is, with field uniformity almost completely defined by the shape of the iron poles, precision in the placement of the current-carrying winding is of much less importance. However, beam optics for high particle energy applications require very strong magnetic fields to control the particle beam. This can best be achieved with superconducting, current-carrying windings, eliminating the requirement for iron which, due to its non-linear magnetization and saturation, would have detrimental effects on field uniformity. Nonetheless, optimal positions have to be determined for the current-carrying conductors and placement of the winding with very high levels of accuracy can result in generation of magnetic fields with improved high field uniformity. In some normal conducting charged particle beam optical systems the magnets for the beam optics have to operate in the presence of high magnetic background fields, in which the iron is fully saturated. In such systems the magnetic field also has to be completely defined by the current-carrying windings.
The current-carrying winding configurations used for charged particle beam optics are typically of cylindrical shape, with the windings surrounding an evacuated tube, also of cylindrical shape, that contains the particle beam. The field-generating winding configurations for such applications, in most cases, consist of multiple saddle shaped layers of winding. Each layer comprises multiple turns of winding as shown in FIGS. 1A and 1B. The shape of the saddle coil winding closely matches the shape of the cylindrical beam tube. Such saddle-shaped winding configurations for generating magnetic fields with a given pole number are typically produced by winding the conductor over itself and around a central island. The present invention is based, in part, on recognition that definition of the winding configuration in a saddle coil magnet (i.e., the conductor path) and accuracy of conductor placement in the winding configuration are critical to acquiring satisfactory or optimal field uniformity, especially in the case of superconducting windings. Other applications of magnetic fields, which are unrelated to charged particle beam optics, also have potential for improved performance based on improved field uniformity. Again, improvements can be realized based on definition of more optimal winding configurations and positioning of the coil conductors to substantially conform to defined configurations in order to produce magnetic fields with acceptable high field uniformity. In the case of rotating electrical machines, e.g., motors and generators, for which torque transfer is achieved with magnetic fields that act between the rotor and the stator, the rotor and stator both produce magnetic fields with various numbers of magnetic poles. For most of these machines, the iron-poles dominate the fields such that minor deviations in placement of coils in the winding configuration has little effect on machine performance. On the other hand, a feature of the invention is that performance of superconducting electrical machines, which provide unmatched power density, can be improved based on more optimal definition of wiring configurations to improve the quality of the magnetic fields. The field uniformity is largely determined by the accuracy of and stability in placement of the coils. As in the case of charged particle beam optics, electrical machines are of cylindrical shape, and saddle-shaped windings have provided an efficient configuration to generate the required magnetic fields. However, if the coils of the rotor or stator windings typically contain lower or higher order harmonics. Another feature of the invention is based on recognition that, in superconducting rotating machines, such resulting non-uniformities in the field can generate torque ripple or vibrations, which will stress shaft bearings and lead to fatigue of these components. For fully superconducting machines, non-uniform fields lead to increased AC losses in the windings, reducing machine efficiency.
According to embodiments a series of conductor assemblies are provided of the type which, when conducting current, generates a magnetic field or which, in the presence of a changing magnetic field, induces a voltage. In one example, a conductor having a spiral configuration is positioned along a path in a cylindrical plane. The conductor extends along an axis central to the cylindrical plane, and positions along the path vary in azimuthal angle. The azimuthal angle of each position is measurable in a plane orthogonal to the axis and relative to a reference point in the plane orthogonal to the axis. The configuration comprises a continuous series of connected turns, Tn, for which n is an integer ranging from one to N. Each turn, Tn, includes a first arc, a second arc and first and second straight segments connected to one another by the first arc. The second arc connects the turn, Tn, to an adjoining turn, Tn+1 or Tn−1. For a given value of n, each of the first and second straight segments in a turn Tn is spaced apart from an adjacent parallel segment in an adjoining turn Tn+1 or Tn−1. For each parallel segment in each turn, Tn, the azimuthal angle, θn, defines a sufficient number of positions according to the relationship
      sin    ⁡          (              m        *                  θ          n                    )        =            n      -              1        2              N  
that all positions along a majority of the length of each straight segment in each turn, Tn, conform to the relationship
      sin    ⁡          (              m        *                  θ          n                    )        =            n      -              1        2              N  
Each first arc in the saddle coil magnet winding structure may conform to the relationship
            F      ⁡              (        x        )              *          sin      ⁡              (                  m          *                      θ            n                          )              =            n      -              1        2              N  
where x is a position along the axis and F(x) varies in value along the arc from zero to one. In one embodiment, some of the positions along the path of a first arc in one of the turns conform to the relationship
            F      ⁡              (        x        )              *          sin      ⁡              (                  m          *                      θ            n                          )              =            n      -              1        2              N  
where x is a position along the axis and F(x) varies in value along the arc from zero to one. Also, each second arc may conform to the relationship
            F      ⁡              (        x        )              *          sin      ⁡              (                  m          *                      θ            n                          )              =                    n        -                  1          2                    N        .  
In the above-described saddle coil magnet winding structure the entire length along each straight segment in each turn, Tn, may conforms to the relationship
      sin    ⁡          (              m        *                  θ          n                    )        =                    n        -                  1          2                    N        .                  and the winding structure may include one or more additional spiral configurations each in a different cylindrical plane concentrically positioned about the axis wherein conductor in each spiral configuration is spaced apart from conductor in each other spiral configuration.        
For an embodiment with the saddle coil magnet winding structure including one or more additional spiral configurations, for each additional configuration:
the azimuthal angle of each position is measurable in a plane orthogonal to the axis and relative to a reference point in the plane orthogonal to the axis, and the configuration comprises a continuous series of connected turns, Tn. Each turn, Tn, includes a first arc, a second arc and first and second parallel segments connected to one another by the first arc. The second arc connects each turn, Tn, to an adjoining turn, Tn+1 or Tn−1.
Also, for each additional configuration of connected turns, Tn, all positions along a majority of the length of each straight segment in each turn, Tn, may conform to
      sin    ⁡          (              m        *                  θ          n                    )        =            n      -              1        2              N  
and the structure may comprise a support body having a groove formed therein and centered about the axis, wherein the first spiral configuration and at least one additional spiral configuration are positioned in the groove. With a first such centered about the axis, a second groove may be formed in the support body, also centered about the axis and spaced away from the first groove, such that at least the first spiral configuration is positioned in the first groove and at least one additional spiral configuration is positioned in the second groove.
In another set of embodiments, a conductor assembly includes a body having a first channel formed therein defining a first path extending along a first cylindrical plane and along a direction parallel to an axis central to the cylindrical plane. The first channel is in a configuration comprising a continuous series of connected turns, GTj, providing a first spiral pattern. A length of conductor comprises two or more electrically connected segments each positioned in the first channel, with a first segment of the conductor positioned in the first cylindrical plane. The first segment provides a first layer of the conductor closest to the axis. Each of the other segments provides an additional layer, with each additional layer positioned over another layer. The body of the conductor assembly may include a second channel formed therein defining a second path extending along a second cylindrical plane and along a direction parallel to an axis central to the cylindrical plane, with the second channel in a configuration comprising a continuous series of connected turns, GTj, providing a second spiral pattern wherein the length of conductor extends from the first spiral pattern into the second spiral pattern with another segment of the conductor positioned in the second channel. Such a segment of the conductor positioned in the second channel may be positioned as a first layer of the conductor in the second channel, with the assembly including one or more additional segments of the conductor in the second channel with each segment in the second channel providing an additional layer of the conductor positioned over another layer of the conductor. Each layer of the conductor may be positioned in a different concentric plane about the axis, and the conductor may be a splice-free wire comprising each of the segments. The body may be insulative, such as the type formed of a fiberglass resin composite material or may be a laminate structure comprising a metal body having an insulative layer formed thereon, or a metal body which receives insulated conductor to provide a helical wiring configuration.
A conductor assembly is also provided in which a conductor having a spiral configuration is positioned along a path in a cylindrical plane and extends along an axis central to the cylindrical plane, with positions along the path varying in azimuthal angle, θn. The azimuthal angle of each position is measurable in a plane orthogonal to the axis and relative to a reference point in the plane orthogonal to the axis. The configuration comprises a continuous series of connected turns, Tn, for which n is an integer ranging from one to N. Each turn, Tn, includes a first arc and a first straight segment. The configuration includes a spacing between at least one turn, Tn, and an adjacent turn Tn+1 or Tn−1. For a given value of n:
(i) a spacing between one of the straight segments in a turn Tn and an adjacent straight segment in an adjoining turn Tn+1 or Tn−1 in the cylindrical plane is determined according to the relationship
      sin    ⁡          (              m        *                  θ          n                    )        =            n      -              1        2              N  
where positions between which the spacing exists are defined by the azimuthal angle, θn, or
(ii) a spacing between one of the arcs in a turn Tn and an adjacent arc in an adjoining turn Tn+1 or Tn−1 in the cylindrical plane is determined according to the relationship
                    F        ⁡                  (          x          )                    *              sin        ⁡                  (                      m            *                          θ              n                                )                      =                  n        -                  1          2                    N        ,
where m is an integer greater than zero, x is a position along the axis and F(x) varies in value along the arc from zero to one, and positions between which the spacing exists are defined by the azimuthal angle, θn. In one variant of this embodiment, the conductor is positioned along a path in a sequence of multiple cylindrical planes, positions along the path in each cylindrical plane vary in azimuthal angle, θn, where in the first cylindrical plane the conductor path begins in an innermost turn and ends in an outermost turn in a first spiral pattern, and in the second cylindrical plane the conductor path begins in an outermost turn and ends in an innermost turn in a second spiral pattern.
According to another embodiment of conductor assemblies of the type which, when conducting current, generates a magnetic field or which, in the presence of a changing magnetic field, induces a voltage, a body has a first channel formed therein defining a first path extending along a first cylindrical plane and along a direction parallel to an axis central to the cylindrical plane (with positions along the path varying in azimuthal angle based on position along the axis) where the first channel is in a configuration comprising a continuous series of connected turns, GTj, providing a first spiral pattern. The configuration comprises a continuous series of connected groove turns, GTj, for which j is an integer ranging from one to N. Each turn, GTj, includes a first arc, a second arc and first and second straight segments connected to one another by the first arc. The second arc connects the turn, GTj to an adjoining turn, GTj+1 or GTj−1. For a given value of n, each of the first and second straight segments in the turn GTj is spaced apart from an adjacent parallel segment in an adjoining turn GTj+1 or GTj−1, and for each straight segment in each turn, GTj, the azimuthal angle, θn, defines a sufficient number of positions according to the relationship
            sin      ⁡              (                  m          *                      θ            n                          )              =                  n        -                  1          2                    N        ,
where m is an integer greater than zero, that all positions along a majority of the length of each straight segment in each turn, GTj, conform to
      sin    ⁡          (              m        *                  θ          n                    )        =                    n        -                  1          2                    N        .  
A related method for constructing a conductor assembly of the type which, when conducting current, generates a magnetic field or which, in the presence of a changing magnetic field, induces a voltage, includes providing a conductor having a spiral configuration, positioned along a path in a first cylindrical plane, which conductor extends along an axis central to the cylindrical plane, with positions along the path varying in azimuthal angle. The azimuthal angle of each position is measurable in a plane orthogonal to the axis and relative to a reference point in the plane orthogonal to the axis. The configuration comprises a first plurality of N turns, Tn, connected to one another in a continuous series in the first cylindrical plane, with each turn, Tn, including first and second coil ends which are each a portion of a turn not parallel with the axis. For a given value of n, each of the turns Tn is spaced apart from an adjacent parallel segment in an adjoining turn Tn+1 or Tn−1, and for each turn, Tn, a sufficient number of positions along a majority of the length of the turn are in accord with the relationship
                    F        ⁡                  (          x          )                    *              sin        ⁡                  (                      m            *                          θ              n                                )                      =                  n        -                  1          2                    N        ,
where m is an integer greater than zero, x is a position along the axis and F(x) varies in value along the coil ends between zero and one, such that all positions along a majority of the length of each turn, Tn, conform to
            F      ⁡              (        x        )              *          sin      ⁡              (                  m          *                      θ            n                          )              =                    n        -                  1          2                    N        .  
In one embodiment of this method all positions along the entire length of each first coil end turn, Tn, may conform to
            F      ⁡              (        x        )              *          sin      ⁡              (                  m          *                      θ            n                          )              =                    n        -                  1          2                    N        .  
Also, all positions along the entire length of a first of the turns, Tn, except for positions along a portion of the second coil end turn, may conform to
            F      ⁡              (        x        )              *          sin      ⁡              (                  m          *                      θ            n                          )              =                    n        -                  1          2                    N        .  
In one embodiment of the method, the step of providing the conductor having a spiral configuration includes providing, as a portion of the second end turn in the first of the turns, a segment which extends to an adjoining turn which segment continues the spiral configuration from the first of the turns to the adjoining turn.
In another embodiment of the method, the step of providing a conductor having a spiral configuration includes positioning the path of the conductor to extend along the axis in a second cylindrical plane concentric with the first cylindrical plane, and the configuration further includes a second plurality of turns connected to one another in a continuous series in the second cylindrical plane, with
positions in the second cylindrical plane varying in azimuthal angle. As a portion of the second end turn in the first of the turns, a segment is provided which extends from the first of the turns to one of the turns in the second cylindrical plane. This segment connects portions of the spiral configuration in the first cylindrical plane with portions of the spiral configuration in the second cylindrical plane.
In still another embodiment of the method, along the path of each turn in the second cylindrical plane, the azimuthal angle, θn, defines a sufficient number of positions according to the relationship
                    F        ⁡                  (          x          )                    *              sin        ⁡                  (                      m            *                          θ              n                                )                      =                  n        -                  1          2                    N        ,
that all positions along a majority of the length of each turn, Tn, conform to
            F      ⁡              (        x        )              *          sin      ⁡              (                  m          *                      θ            n                          )              =                    n        -                  1          2                    N        .  
Also according to the invention, a length of conductor extends in a continuous spiral pattern in a first cylindrical plane extending along a central axis to create a saddle coil shape. The pattern comprises N turns, Tn, with each turn having a fixed position in the same cylindrical plane, each turn including a pair of straight segments parallel to one another. The straight segments are arranged in spaced-apart relation as a function of azimuthal angle, θn, about the axis, according to
      sin    ⁡          (              m        *                  θ          n                    )        =            n      -              1        2              N  
where m is an integer greater than zero and the azimuthal angle, θn, of each position along each straight segment is measured in a plane orthogonal to the axis and relative to a reference point in the plane orthogonal to the axis.
In a method of forming a conductor assembly of the type which, when conducting current, generates a magnetic field or which, in the presence of a changing magnetic field, induces a voltage,
(i) a series of closed conductor paths, n, is defined, where n ranges from 1 to N. All of the closed paths reside in one cylindrical plane positioned about an axis in accord with the relationship
            F      ⁡              (        x        )              *          sin      ⁡              (                  m          *                      θ            n                          )              =                    n        -                  1          2                    N        .  
where m is an integer value greater than one, and θ is the azimuthal angle of each position, measured in a plane orthogonal to the axis and relative to a reference point in the plane orthogonal to the axis, the relationship providing a suitable approximation for an ideal current density distribution according to cos(mθ), where x is a position along the axis and F(x) is a shape function which varies in value from zero to one;
(ii) a set of conductive winding turns is created by modifying the contours of the closed conductor paths with respect to the axial direction, X, to transform the closed shapes into a set of open shapes which each connect to another open shape to create a spiral configuration which departs from the ideal current density distribution.
In one embodiment the open shapes are spiral turns created by modifying the lengths of straight sections in closed shapes or by modifying the curvature imparted by the shape function F(x), with respect to position along the axis. This imparts a spiral shape that connects with a straight section in a portion of an adjacent conductor shape in the set of open shapes.
There is also provided a method for constructing a conductor assembly of the type which, when conducting current, generates a magnetic field or which, in the presence of a changing magnetic field, induces a voltage. A conductor is provided in a spiral configuration, positioned along a path in a first cylindrical plane, which conductor extends along an axis central to the cylindrical plane, positions along the path varying in azimuthal angle. The azimuthal angle of each position is measured in a plane orthogonal to the axis and relative to a reference point in the plane orthogonal to the axis. The configuration comprises a first plurality of N turns, Tn, connected to one another in a continuous series in the first cylindrical plane, each turn, Tn, including first and second coil ends which are each a portion of a turn not parallel with the axis. For a given value of n, each of the turns Tn is spaced apart from an adjacent turn Tn+1 or Tn−1, and, for at least one turn, Tn, the positions along a majority of the length of the turn are in accord with the afore-defined relationship
                    F        ⁡                  (          x          )                    *              sin        ⁡                  (                      m            *                          θ              n                                )                      =                  n        -                  1          2                    N        ,
wherein multipole content which would otherwise be present in a field generated by the spiral configuration, relative to a pure multipole field of order m, which would theoretically be generated by a configuration having an ideal cos(nθ) current distribution, is reduced by applying a numerical optimization technique which modifies the shapes of turns to more closely conform the field pattern generated by the spiral configuration to the pure multipole field of order m.
In a method for constructing a conductor assembly of the type which, when conducting current, generates a magnetic field or which, in the presence of a changing magnetic field, induces a voltage, with a channel in the assembly having a spiral configuration for a multipole field configuration of order m. The method includes inserting multiple layers of the conductor in the channel to conform each layer of the conductor to the spiral configuration, with each layer of the conductor positioned along a path in a different one of multiple concentric cylindrical planes, which paths extend along an axis central to the cylindrical planes, positions along the paths varying in azimuthal angle. Each layer in the configuration comprises a plurality of N turns, Tn, connected to one another in a continuous series in the first cylindrical plane. Each turn, Tn, includes first and second coil ends which are each a portion of a turn not parallel with the axis, and, for a given value of n, each of the turns Tn is spaced apart from an adjacent turn Tn+1 or Tn−1. Paths are defined for straight portions of the channel or for curved portions of the channel, which result in path segments which deviate from ideal channel path segments, into which one or more segments of conductor turns in one or more conductor layers are placed. In one embodiment, for at least one turn, Tn, the positions along a majority of the length of the turn are in accord with the relationship
                    F        ⁡                  (          x          )                    *              sin        ⁡                  (                      m            *                          θ              n                                )                      =                  n        -                  1          2                    N        ,
where m is an integer greater than zero, x is a position along the axis and F(x) varies in value along the coil ends between zero and one. In one embodiment multipole content which would otherwise be present in a field generated by the spiral configuration, relative to a pure multipole field of order m (which would theoretically be generated by a configuration having an ideal cos(mθ) current distribution), is reduced by applying a numerical optimization technique which modifies the shapes of turns to more closely conform the field pattern generated by the spiral configuration to the pure multipole field of order m. The numerical optimization technique may modify the shapes of turns to more closely conform the field generated by the spiral configuration to the multipole field which would theoretically be generated by a configuration having an ideal cos(mθ) current distribution.
A conductor assembly is also provided which comprises a body member having a series of spaced-apart, concentric channels formed therein, with each channel formed in a different one of multiple concentric cylindrical planes formed about a central axis. A conductor is positioned in each of the channels with multiple layers of the winding stacked in each channel. The conductor may be formed in a saddle coil spiral configuration. In a related method for making a multi-level conductive winding, a series of concentric channels is formed about an axis of a body member, with each channel passing through a different cylindrical plane and extending in a radial direction away from the axis. Multiple layers of conductor are placed within each of the channels with each layer positioned in a different concentric cylindrical plane. The winding may be a continuous, splice-free element.
Also according to the invention, a configuration is provided for a conductive winding of the type which, when conducting current, generates a magnetic field or which, in the presence of a changing magnetic field, induces a voltage. A conductor having a spiral shape comprising turns, Tn, is positioned along a path in a first cylindrical plane. The conductor extends along an axis central to the cylindrical plane, with positions along the path varying in azimuthal angle. Each turn, Tn, includes a first arc, a second arc and first and second straight segments. A first turn Tn and a second turn Tn+1 or Tn−1 adjoin one another in the series and are spaced apart from one another, with a first segment of the conductor in the first turn and a second segment of the conductor in the second turn Tn+1 or Tn−1 each following a path in accord with
            F      ⁡              (        x        )              *          sin      ⁡              (                  m          *                      θ            n                          )              =            n      -              1        2              N  
where m is an integer greater than zero, x is a position along the axis and F(x) varies in value along the coil ends between zero and one. The conductor further comprises a third segment which does not follow a path in full accord with
                    F        ⁡                  (          x          )                    *              sin        ⁡                  (                      m            *                          θ              n                                )                      =                  n        -                  1          2                    N        ,
the third segment providing electrical connection between the first and second segments. In one embodiment of this configuration the first segment of the conductor in the first turn is an arc. The second segment of the conductor in the second turn may be an arc. The first segment of the conductor in the first turn may be a straight segment and the second segment of the conductor in the second turn may be a straight segment.
Also in a channel configuration for a conductive winding of the type which, when conducting current, generates a magnetic field or which, in the presence of a changing magnetic field, induces a voltage, a spiral channel is formed in a body comprising a continuous series of connected channel turns, GTn, positioned along a path in a first cylindrical plane, which channel extends along an axis central to the cylindrical plane, with positions along the path varying in azimuthal angle. Each turn, GTn, includes a first arc, a second arc and first and second straight segments.
A first turn GTn and a second turn GTn+1 or GTn−1 adjoin one another in the series. A first segment of the channel in the first turn GTn and a second segment of the channel in the second turn GTn+1 or GTn−1 each follow a path in accord with
                    F        ⁡                  (          x          )                    *              sin        ⁡                  (                      m            *                          θ              n                                )                      =                  n        -                  1          2                    N        ,
where m is an integer greater than zero, x is a position along the axis and F(x) varies in value along each of the arcs between zero and one. The channel further comprises a third segment which does not follow a path in accord with
            F      ⁡              (        x        )              *          sin      ⁡              (                  m          *                      θ            n                          )              =                    n        -                  1          2                    N        .  
The third segment provides a path for a conductive segment to provide electrical connection between conductor in the first and second segments. The first segment of the channel in the first turn or in the second turn may be an arc or a straight segment.
In another configuration for a conductive winding of the type which, when conducting current, generates a magnetic field or which, in the presence of a changing magnetic field, induces a voltage, a conductor has a spiral pattern comprising a first continuous series of connected turns positioned along a path in a first cylindrical plane, and at least a second continuous series of connected turns positioned along a path in a second cylindrical plane. The conductor extends along an axis central to the cylindrical plane, with positions along the path varying in azimuthal angle. Each turn includes a first arc, a second arc and first and second straight segments. The azimuthal angle of each position is measurable in a plane orthogonal to the axis and relative to a reference point in the plane orthogonal to the axis. A first segment of the conductor in a first turn in the first continuous series in the first cylindrical plane and a second segment of the conductor in the second continuous series in the second cylindrical plane each follow a path in accord with
                    F        ⁡                  (          x          )                    *              sin        ⁡                  (                      m            *                          θ              n                                )                      =                  n        -                  1          /          2                    N        ,
where m is an integer greater than zero, x is a position along the axis and F(x) varies in value along the coil ends between zero and one. The conductor further comprises a third segment which does not follow a path in accord with
            F      ⁡              (        x        )              *          sin      ⁡              (                  m          *                      θ            n                          )              =                    n        -                  1          /          2                    N        .  
The third segment provides electrical connection between the first and second segments. The first segment of the conductor in the first turn or in the second turn may be an arc or a straight segment.
In a channel configuration for a conductive winding a spiral channel formed in a body includes a first continuous series of connected channel turns positioned along a path in a first cylindrical plane, and at least a second continuous series of connected channel turns positioned along a path in a second cylindrical plane, which channel extends along an axis central to the cylindrical plane. Positions along the path vary in azimuthal angle. Each channel turn includes a first arc, a second arc and first and second straight segments. The azimuthal angle of each position is measured in a plane orthogonal to the axis and relative to a reference point in the plane orthogonal to the axis. The first segment of the channel in a first turn in the first continuous series in the first cylindrical plane and a second segment of the channel in the second continuous series in the second cylindrical plane each follow a path in accord with
                    F        ⁡                  (          x          )                    *              sin        ⁡                  (                      m            *                          θ              n                                )                      =                  n        -                  1          /          2                    N        ,
where m is an integer greater than zero, x is a position along the axis and F(x) varies in value along the coil ends between zero and one. The channel further comprises a third segment which does not follow a path in accord with
                    F        ⁡                  (          x          )                    *              sin        ⁡                  (                      m            *                          θ              n                                )                      =                  n        -                  1          /          2                    N        ,
the third segment providing a path for a conductive segment to provide electrical connection between conductor in the first and second segments. The first segment of the channel in the first turn or the second turn may be an arc or a straight segment.
A method of fabricating a spiral winding structure includes defining a spiral shaped channel about an axis in a body to provide a path. The channel comprises a series of N spaced apart and connected channel turns Tn (n=1 to N), each channel turn having a first arc, a second arc and first and second straight segments, where spacings between adjoining turns in the series are in accord with
                    F        ⁡                  (          x          )                    *              sin        ⁡                  (                      m            *                          θ              n                                )                      =                  n        -                  1          /          2                    N        ,
along the majority of each channel turn. A conductive material is conformed to the path of the spiral shaped channel, wherein m is an integer greater than zero, θn is an angle measured in a plane orthogonal to the axis and relative to a reference point in the plane orthogonal to the axis, x is a position along the axis, and F(x) varies in value along each arc between zero and one.
Also according to the invention, a structure includes at least first and second layers positioned about one another and two or more conductor portions, each conductor portion positioned along a different one of the layers, the first of the conductor portions in a first cylindrical plane centered about an axis and the second of the conductor portions in a second cylindrical plane also centered about the axis, with the second plane a greater distance from the axis than the first cylindrical plane, wherein at least the first and second conductor portions are segments in a continuous conductive path extending from along the first of the layers to along at least the second of the layers. The conductive path is arranged so that when conducting current a magnetic field can be generated or so that when, in the presence of a changing magnetic field, a voltage is induced. The first and second conductor portions each have a spiral configuration positioned along the path in one of the cylindrical planes and each extend along the axis, with positions along the path varying in azimuthal angle. Each conductor portion comprises a continuous series of connected turns, Tn, for which n is an integer ranging from one to N. Each turn, Tn, includes a first arc, a second arc and first and second straight segments connected to one another by the first arc. The second arc connects the turn, Tn, to an adjoining turn, Tn+1 or Tn−1. In one embodiment of the structure of claim 160 the first and second conductor portions are each positioned in a groove formed in one of the first and second layers which groove defines positions of each conductor portion along the path. For a given value of n, each of the first and second straight segments in a turn Tn may be spaced apart from an adjacent straight segment in an adjoining turn Tn+1 or Tn−1. For each straight segment in each turn, Tn, the azimuthal angle, θn, may define a sufficient number of positions according to the relationship
      sin    ⁡          (              m        *                  θ          n                    )        =            n      -              1        /        2              N                  that all positions along a majority of the length of each straight segment in each turn, Tn, conform to        
      sin    ⁡          (              m        *                  θ          n                    )        =            n      -              1        /        2              N  
In one embodiment of the structure each first arc in one of the conductor portions conforms to the relationship
                    F        ⁡                  (          x          )                    *              sin        ⁡                  (                      m            *                          θ              n                                )                      =                  n        -                  1          /          2                    N        ,
where x is a position along the axis and F(x) varies in value along the arc from zero to one, and in another embodiment all positions along a majority of the length of each turn, Tn, in one of the conductor portions conforms to the relationship
            F      ⁡              (        x        )              *          sin      ⁡              (                  m          *                      θ            n                          )              =                    n        -                  1          /          2                    N        .  
In another embodiment fewer than all positions along the length of each turn, Tn, conform to the relationship
            F      ⁡              (        x        )              *          sin      ⁡              (                  m          *                      θ            n                          )              =                    n        -                  1          /          2                    N        .  
A configuration for a conductive winding includes a length of conductor and a spiral channel in which two or more layers of the conductor are positioned, one layer over another layer, the channel including a first series of N connected channel turns formed in a portion of a body, the turns positioned along a path so that the channel extends along an axis, the channel having a depth extending in a radial direction with respect to the axis to contain the two or more layers. The configuration may include J layers of conductor in the channel each electrically connected in series to another layer in the channel to provide one conductor having J*N turns. Each of the layers of conductor may be positioned in a different one of multiple concentric cylindrical planes about the axis. The conductor may be continuous and splice free. Further, the configuration may include a second spiral channel in which two or more additional layers of the conductor are positioned, one layer over another layer, the second channel including a second series of connected channel turns formed in another portion of the body in a cylindrical plane positioned radially outward from the first series of connected channel turns with respect to the axis, the second channel having a depth extending in a radial direction with respect to the axis to contain the additional layers. The body in which the channel is formed may be a layer of insulative material or a layer of conductive material.
A method of forming a conductive winding includes forming a spiral channel in a portion of a body in which two or more layers of conductor are to be positioned, one layer over another layer. The channel includes a first series of connected channel turns, with the turns positioned along a path so that the channel extends along an axis. The channel has having a depth extending in a radial direction with respect to the axis to contain the two or more layers, the turns each comprising a straight section of the channel path and a curved section of the channel path, wherein the straight sections are formed with parallel channel walls by cutting into the body with a saw blade. A length of conductor is positioned in the channel by laying one portion of the length over another portion of the conductor length to provide one conductive layer over another conductive layer. The step of cutting into the body with a saw blade may provide a cut in a single path or a single pass to define the entire depth of the channel instead of requiring multiple paths of a cutting tool to machine the full depth of the channel to accommodate two or more layers of the conductor.
A method is provided for securing multiple layers of conductor in a single channel. A channel is formed in a spiral configuration comprising a series of channel turns with the channel having a restricted opening of a first dimension smaller than a thickness dimension of the conductor. A first portion of the conductor is pushed through the restricted channel opening with application of a force so that the channel receives the conductor to create a first level of conductor turns in the channel turns. A second portion of the conductor is also pushed through the restricted channel opening with application of a force so that the channel receives a portion of the conductor to create a second level of conductor turns in the channel turns. The step of pushing the first portion of the conductor through the restricted channel opening may expand or deform the dimension of the channel opening, allowing a portion of each conductor turn to be pushed through the opening, after which the dimension of the opening may revert from an expanded dimension to a size which is substantially the same as the first dimension. Also, the thickness dimension of the conductor may be the smallest dimension of the conductor and the difference between the first dimension of the restricted opening and the thickness dimension of the conductor may be between seven and nine percent.
According to a method of forming a channel with a restricted opening that secures multiple layers of conductor in a single channel, a channel is formed in a spiral configuration comprising a series of channel turns with the channel having a restricted opening of a first dimension smaller than a thickness dimension of the conductor by providing a first cut to a body to create a first width for an opening in the channel through which portions of the conductor are received into the channel. The thickness dimension may be the smallest dimension of the conductor. A second cut is made to create a second width in the channel larger than the first width. The first cut and the second cut may each be created with a tool and each may be created with a different tool. The first cut may create the majority of the depth of the channel to receive multiple layers of conductor with one layer stacked over another layer. Also, the first cut may provide a uniform width along a path defined by multiple ones of the channel turns, and the second cut may create a second width in the channel larger than the first width without altering the width of the opening.
In a method of forming a channel with a restricted opening a channel is formed which has a spiral configuration comprising a series of channel turns with the channel having a restricted opening of a first dimension smaller than a thickness dimension of the conductor by providing a first cut to a body to create an initial opening. At least a portion of the channel with the initial opening has a first width and a portion of the interior of the channel also has the first width. The initial opening is covered with a layer of removable material and a second cut creates the restricted opening through the layer of removable material. The restricted opening has the second width which is smaller than the first width. The first cut and the second cut may each be each created with a different tool, and the first cut may create the majority of the depth of the channel to receive multiple layers of conductor with one layer stacked over another layer. The first cut may provide a uniform channel width along a path defined by multiple ones of the channel turns, and the second cut may provide a uniform width to the restricted opening along a path defined by multiple ones of the channel turns.
Another configuration for a conductive winding is also of the type which, when conducting current, generates a magnetic field or which, in the presence of a changing magnetic field, induces a voltage. This configuration includes a length of conductor and a spiral channel which accommodates two or more layers of the conductor for positioning therein, with one layer positioned over another layer. The channel includes a series of connected channel turns formed in a portion of a body, with the turns positioned along a path so that the channel extends along an axis, the channel having a depth extending in a radial direction with respect to the axis to contain the two or more layers. The channel includes a series of shaped repository openings along walls of the channel. Each repository opening is positioned a different radial distance from the axis to provide a series of repository positions, with one or more of the repository positions positioned over another one of the repository positions. Each repository opening is of a dimension smaller than a thickness dimension of the conductor to restrict passage of the conductor into an adjoining repository position such that a force must be applied to push the conductor through the repository opening and into the repository position. In one embodiment each repository opening is positioned in a different one of several cylindrical planes concentrically positioned about the axis. The conductor may be a splice-free continuous length, with a different portion of the conductor occupying a different repository position to provide a series of winding turns in each of several cylindrical planes concentrically positioned about the axis. In a set of embodiments, one or more of the repository spacers is formed in the channel walls.
According to a method of manufacturing a conductive winding of the type which, when conducting current, generates a magnetic field or which, in the presence of a changing magnetic field, induces a voltage, a spiral channel is created in a portion of a body, which channel accommodates two or more layers of conductor for positioning therein, one layer over another layer. The channel includes a series of connected channel turns formed in a portion of the body, and the turns are positioned along a path so that the channel extends along an axis. The channel has a depth extending in a radial direction with respect to the axis to contain the two or more layers, and the channel includes a series of shaped repository openings along walls of the channel, with each repository opening formed a different radial distance from the axis to provide a series of repository positions, with one or more of the repository positions positioned over another one of the repository positions. Each repository opening is of a dimension smaller than a thickness dimension of the conductor to restrict passage of the conductor into an adjoining repository position such that a force must be applied to push the conductor through the repository opening and into the repository position. Segments of the conductor are sequentially passed through one or more of the repository openings to place each segment in one repository position to create a multi-level helical winding path in a single groove. By sequentially passing segments of the conductor through the repository openings it is possible to position different levels of conductor segments in different spaced-apart cylindrical planes positioned about the axis. In a related embodiment a space is provided between a first repository position and a second repository position. The space provides for heat exchange to serve as a cooling channel for conductor in the first and second repository positions.
In a related method for providing cooling channels in a groove containing multiple levels of conductor, shaped repository openings are created along walls of the groove, which openings define repository positions for different layers of conductor placed in the groove and constrain movement of the conductor. A space is provided between a first repository position and a second repository position, and at least two segments of conductor are passed through one or more of the repository openings to position a first segment in the first repository position and to position a second segment in the second repository position. A space between the first repository position and the second repository position is retained without containing another segment of conductor positioned between the first and second segments. The space may provide for heat exchange and serve as a cooling channel for conductor in the first and second repository positions. The space may be formed in the shape of a repository opening and be positioned between the first repository opening and the second repository opening.
In a method of constructing a conductor assembly of the type which, when conducting current, generates a magnetic field or which, in the presence of a changing magnetic field, induces a voltage, a wiring assembly is configured as a series of spaced-apart spiral configurations of conductor with each configuration positioned in a different one of multiple cylindrical planes each centered about a common axis. Each spiral configuration includes a plurality of conductor turns. The step of configuring the wiring assembly includes positioning segments of the conductor to provide turn-to-turn transitions which connect turns in the same plane to form a multi-turn helical geometry in each plane. Conductor segments also extend out of the cylindrical planes to conductively connect pairs of spiral configurations of conductor in the adjoining cylindrical planes to form one continuous multi-level winding configuration. In the disclosed embodiments the step of positioning segments of the conductor to provide turn-to-turn transitions within each multi-turn helical geometry only positions each of extended conductor segments within the cylindrical plane in which the multi-turn helical geometry is disposed. The step of providing the turn-to-turn transitions to connect turns in each plane may form a multi-turn helical geometry in each plane.
A wiring assembly according to the invention includes a series of spaced-apart spiral configurations of conductor with each configuration positioned in a different one of multiple cylindrical planes each centered about a common axis. Each spiral configuration comprises a plurality of conductor turns, wherein the conductor includes
(i) segments positioned to provide turn-to-turn transitions which connect turns in each plane to form a multi-turn helical geometry in each plane; and
(ii) segments positioned out of the cylindrical planes to conductively connect pairs of spiral configurations of conductor in the adjoining cylindrical planes to form one continuous multi-level winding configuration. In one embodiment the turns in each of the spaced-apart spirals are serially connected to one another and are otherwise spaced apart from one another. In another embodiment all of the turns in each of the spaced-apart spirals are continuous and splice-free conductor.
A wiring assembly of the type which, when conducting current, generates a magnetic field or which, in the presence of a changing magnetic field, induces a voltage, is formed with a series of spaced-apart spiral configurations of conductor each positioned along a common cylindrical plane centered about an axis with each configuration having multiple layers of winding. A series of conductor segments provide electrical connections between one or more pairs of the spaced apart configurations. Layout of one or more pairs of the conductor segments which effect the connections measurably offset magnetic field magnitudes of order m generated by each conductor segment when the segments are conducting current. In an embodiment of this wiring assembly:                (i) a first conductor segment is positioned to carry current in a clockwise direction to or from one configuration and has a first field contribution of order m when carrying the current and a second conductor segment is positioned to carry current in a counterclockwise direction to or from another configuration and has a second field contribution of order m when carrying the current,        (ii) at a position along the axis, when the segments are conducting current, the first field contribution of order m and the second field contribution of order m are additive to provide a measurable net magnitude of the combined first field contribution of order m, and        (iii) the first and second conductor segments are positioned in sufficient proximity of one another that the magnitude of the net field contribution of order m resulting from the combined contributions of the first and second segments is less than the sum of the magnitudes of the individual field contributions of order m generated by each segment. In an embodiment of this assembly the first and second conductor segments are positioned in sufficient proximity of one another that the magnitude of the net field contribution of order m resulting from the combined contributions of the first and second segments is less than the magnitudes of the individual field contribution of order m generated by either segment. For each configuration, the layers of winding each comprise a series of turns and the layers may each be positioned in a different one of multiple cylindrical planes each centered about the axis.        
In an assembly of the type which, when conducting current, generates a magnetic field or which, in the presence of a changing magnetic field, induces a voltage, a winding configuration includes multiple layers of conductor where each layer is a helically shaped, comprising a conductive material formed along a different cylindrical plane. Each of the cylindrical planes is centered about a common axis wherein the conductive material in each layer is electrically connected to conductive material in the other layers to provide a multi-layer helical winding configuration. In one embodiment the winding configuration is in the shape of a saddle coil. Each helically shaped layer may comprise a series of connected turns of the conductive material and the turns may be spaced apart from one another. The winding configuration may be in the shape of a multilayer saddle coil and each helically shaped layer may comprise a segment of conductor machined or otherwise patterned into a layer of conductive turns of a saddle coil geometry, and contact surfaces of conductor segments in adjacent ones of concentric coil rows may come into direct contact with one another to effect current flow from layer to layer.
Concentric coil rows may be laminate structures comprising a conductive material deposited thereon. Such laminated concentric coil rows may be cylindrically shaped bodies each comprising m spaced-apart winding configurations with each winding configuration approximating a cos(mθ) current density relationship as a function of position along each winding configuration, where m is an integer value greater than zero and θ is an azimuthal angle measured about the axis. Each winding configurations may have a conductive material deposited thereon and patterned to form a helically shaped layer.
A method is provided for forming a superconductor in a channel having a spiral path comprising. Chemical precursor material for synthesizing the superconductor is placed in a tube. The tube containing the chemical precursor materials is placed in the channel. The precursor material is chemically reacted in the tube after the tube is placed in the groove to synthesize the superconductor in situ. The tube may comprise a combination of a barrier metal and a stabilizing metal. In one embodiment the superconductor is MgB2, the tube comprises copper and a surface along the inside of the tube is plated with niobium.
A method is also disclosed for fabricating a superconducting assembly which forms a superconducting material in situ during fabrication of a winding configuration. The assembly may, when conducting current, generate a magnetic field or, in the presence of a changing magnetic field, induce a voltage. According to the method precursor materials for synthesizing the superconducting material are mixed together in stoichiometric proportions. A plurality of channels are created in a support structure with each channel positioned along a different cylindrical plane but centered about a common axis, Each channel comprises multiple helically shaped turns connected to one another. The mixed precursor materials are placed in each of the channels and reacted to synthesize the superconductor in the channels. According to disclosed embodiments, the superconductor material in each channel of helically shaped layer is electrically connected to superconductor material in another of the channels to provide a multi-layer helical winding configuration. Multiple ones of the channels containing the precursor material may be sequentially formed in different cylindrical planes about the axis and then simultaneously heated to create a series of concentric channels each filled with one or more superconductive segments of wire. Also, the step of sequentially forming the channels may include:
initially forming each of the channels as a groove in a layer of material, each groove having an opening into which the precursor material is placed; and after placing the precursor material in the groove, covering the opening with another layer of material which closes the opening and provides further material in which another channel can be formed.
There is also presented another method for fabricating a superconducting assembly which forms superconducting material in situ during fabrication of a winding configuration. The precursor for synthesizing the superconducting material are mixed in stoichiometric proportions. A plurality of ports is created with each port positioned along a different cylindrical plane but centered about a common axis, with each channel comprising multiple helically shaped turns connected to one another. The mixed precursor materials are placed in each of the channels by causing the mixed precursor materials to flow into each port with a carrier liquid. The carrier liquid is allowed to evaporate so that the precursor materials build up along walls of the ports. The support structure is heated to chemically synthesize the superconductor material in the ports. The synthesized superconducting material may comprise MgB2.
Another method for fabricating a superconducting assembly forms superconducting material in situ during fabrication of a winding configuration. An open channel is formed in a support structure followed by sequentially forming in the channel (i) a metal layer (e.g., copper) along a channel wall, (ii) a barrier layer (e.g., niobium) over the metal layer, and a first mixture of precursor materials in stoichiometric proportions over the barrier layer. The precursor materials are then heated to chemically synthesize a first layer of superconductor material in the channel. The mixture of precursor materials may be repeatedly injected, dried and compacted in the channel. The step of forming in the channel the mixture of precursor materials may include injecting a slurry containing the precursor materials in the channel. The method may also include forming over the first mixture of precursor materials an insulative layer, and then the repeating the steps of forming in the channel (i) a metal layer along a channel wall, (ii) a barrier layer over the metal layer, and a mixture of precursor materials in stoichiometric proportions over the barrier layer, followed by heating the precursor materials to form a second layer of superconductor material in the channel which is electrically isolated from the first layer of superconductive material. Also, the method may include that step of sealing the channel with silicon oxide or ceramic material before progressing to next level.
In numerous embodiments channels or ports may be formed with variable cross sections and the area in cross section of the superconductor material may be increased along curved portions of turns in helical wiring configurations to limit maximum current density or avoid reaching critical field levels when the assembly carries current through the superconducting material.
Portions of support structures on which wiring configurations are formed may be insulative and incorporate ceramic or glass fiber material in a resin composite to modify the temperature characteristics or mechanical properties of the support structure.
According to other embodiments a configuration for a superconducting winding, of the type which, when conducting current, generates a magnetic field or which, in the presence of a changing magnetic field, induces a voltage, includes a spiral channel which accommodates two or more layers of the superconductor material for positioning therein, one layer over another layer. The channel includes a series of connected channel turns formed in a portion of a body. The turns are positioned along a path so that the channel extends along an axis, the channel having a depth extending in a radial direction with respect to the axis to contain the two or more layers. The channel includes a series of shaped repository openings along walls of the channel, and each repository opening is positioned a different radial distance from the axis to provide a series of repository positions. One or more of the repository positions is positioned over another one of the repository positions, and each repository opening is of a dimension smaller than a thickness dimension of the conductor to be passed therethrough to restrict passage of each conductor into an adjoining repository position such that a force must be applied to push the conductor through the repository opening and into the repository position. The configuration includes
(i) a first segment of copper conductor positioned in a first repository position closest to the axis;
(ii) a first barrier layer formed on a surface of the copper conductor;
(iii) a first mixture of precursor material for synthesizing the superconductor material in a second repository position over the first repository position;
(iv) an insulative space over the second repository position;
(v) a second segment of copper conductor positioned in a third repository position positioned over the second repository position;
(vi) a second barrier layer formed on a surface of the second segment of copper conductor;
(viii) a second mixture of precursor material for synthesizing the superconductor material in a fourth repository position over the third repository position; and
(ix) an insulative layer over the fourth repository position.
The first segment of copper conductor may be a body of copper wire inserted into the first repository position, or deposited copper formed in the first repository position.